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Beliebt Rechnen >

(dx)/(dt)=k^1(1-x)+k^2(1-x)^2

Lösung

\frac{d x}{d t} = k^{1} \cdot (1 - x) + k^{2} \cdot (1 - x)^{2}

Lösung

x = \frac{e ^{k t + c_{1}}}{- 1 + e ^{k t + c_{1}}} - \frac{1}{- 1 + e ^{k t + c_{1}}} - \frac{1}{k ( - 1 + e ^{k t + c_{1}} )}

Schritte zur Lösung

\frac{d x}{d t} = k^{1} \cdot (1 - x) + k^{2} \cdot (1 - x)^{2}

Solve separable ODE:

x = \frac{e ^{k t + c_{1}}}{- 1 + e ^{k t + c_{1}}} - \frac{1}{- 1 + e ^{k t + c_{1}}} - \frac{1}{k ( - 1 + e ^{k t + c_{1}} )}

x = \frac{e ^{k t + c_{1}}}{- 1 + e ^{k t + c_{1}}} - \frac{1}{- 1 + e ^{k t + c_{1}}} - \frac{1}{k ( - 1 + e ^{k t + c_{1}} )}

Graph

Beliebte Beispiele

y^{^{'}} = y \cdot y

y=3^{ln(x)}(dy)/(dx)

y = 3^{l n (x)} \frac{d y}{d x}

y^'=e^{(2+4)x+(1+3)y}

y^{^{'}} = e^{(2 + 4) x + (1 + 3) y}

y^{^{'}} = - y (1 - y)

y^{^{'}} - sin (y) = 1